Critical behavior of the two-dimensional random-bond Potts model: a short-time dynamic approach

Short-time critical dynamics of damage spreading in the two-dimensional Ising model

The short-time critical dynamics of propagation of damage in the Ising ferromagnet in two dimensions is studied by means of Monte Carlo simulations. Starting with equilibrium configurations at T=∞ and magnetization M=0 , an initial damage is created by flipping a small amount of spins in one of the two replicas studied. In this way, the initial damage is proportional to the initial magnetization M0 in one of the configurations upon quenching the system at T C, the Onsager critical temperature of the ferromagnetic-paramagnetic transition. It is found that, at short times, the damage increases with an exponent θ D=1.915(3) , which is much larger than the exponent θ=0.197 characteristic of the initial increase of the magnetization M(t). Also, an epidemic study was performed. It is found that the average distance from the origin of the epidemic (R2(t)) grows with an exponent z∗ ≈ η ≈ 1.9, which is the same, within error bars, as the exponent θ D. However, the survival probability of the epidemics reaches a plateau so that δ=0. On the other hand, by quenching the system to lower temperatures one observes the critical spreading of the damage at T D ≃ 0.51TC, where all the measured observables exhibit power laws with exponents θ D=1.026(3), δ=0.133(1), and z∗=1.74(3).

Logarithmic correction to scaling in domain-wall dynamics at Kosterlitz-Thouless phase transitions

With Monte Carlo simulations, we investigate the relaxation dynamics of domain walls at the Kosterlitz-Thouless phase transition, taking the two-dimensional XY model as an example. The dynamic scaling behavior is carefully analyzed, and a domain-wall roughening process is observed. Two-time correlation functions are calculated and aging phenomena are investigated. Inside the domain interface, a strong logarithmic correction to scaling is detected.

Critical dynamics of the two-dimensional random-bond Potts model with nonequilibrium Monte Carlo simulations

We study two-dimensional q -state random-bond Potts models for both q=8 and q=5 with a linearly varying temperature. By applying a successive Monte Carlo renormalization group procedure, both the static and dynamic critical exponents are obtained for randomness amplitudes (the strong to weak coupling ratio) of r_{0}=3 , 10, 15, and 20. The correlation length exponent nu increases with disorder from less than to larger than unity and this variation is justified by the good collapse of the specific heat near the critical region. The specific heat exponent is obtained by the usual hyperscaling relation alpha=2-dnu and thus indicates no possibility of the activated dynamic scaling. Both r_{0} and q have effects on the critical dynamics of the disordered systems, which can be seen from variations of the rate exponent, the hysteresis exponent, and the dynamic critical exponent. Implications of these results are discussed.

Short-time critical dynamics at perfect and imperfect surfaces

With Monte Carlo simulations, we study the dynamic relaxation at perfect and imperfect surfaces of the three-dimensional Ising model with an ordered initial state. The time evolution of the surface magnetization, the line magnetization of the defect line, and the corresponding susceptibilities and second cumulants is carefully examined. Universal dynamic scaling forms including a dynamic crossover scaling form are identified at the ordinary, special, and surface phase transitions. The critical exponents beta1 of the surface magnetization and beta2 of the line magnetization are extracted. The impact of the defect line on the universality classes is investigated.

Nonequilibrium critical dynamics with domain wall and surface

With Monte Carlo simulations, we investigate the relaxation dynamics with a domain wall for magnetic systems at the critical temperature. The dynamic scaling behavior is carefully analyzed, and a dynamic roughening process is observed. For comparison, similar analysis is applied to the relaxation dynamics with a free or disordered surface.

Short-time critical dynamics and aging phenomena in the two-dimensional XY model

With Monte Carlo methods, we simulate dynamic relaxation processes of the two-dimensional XY model at the Berezinskii-Kosterlitz-Thouless phase transition temperature and below, starting from both ordered and disordered initial states. The two-time correlation function A(t',t) is measured, and aging phenomena are investigated. The power-law correction in the spatial correlation length xi(t) for relaxation with an ordered initial state and the logarithmic correction for relaxation with a disordered initial state are carefully analyzed. The scaling functions of A(t',t) are then extracted.

Dynamic Monte Carlo simulations of the three-dimensional random-bond Potts model

The effect of random bonds on the phase transitions of the three-dimensional three-state Potts model is investigated with extensive dynamic Monte Carlo simulations. In the weakly disordered regime, the phase diagram is obtained with a recently suggested nonequilibrium reweighting method. The tricritical point separating the first- and second-order transitions is determined, and the critical exponents of the continuous phase transition induced by quenched randomness are estimated.